Abstract
We develop a detailed theoretical framework for various types of transcription factor gene oscillators. We further demonstrate that one can build genetic-oscillators which are tunable and robust against perturbations in the critical control parameters by coupling two or more independent Goodwin-Griffith oscillators through either -OR- or -AND- type logic. Most of the coupled oscillators constructed in the literature so far seem to be of -OR- type. When there are transient perturbations in one of the -OR- type coupled-oscillators, then the overall period of the system remains constant (period-buffering) whereas in case of -AND- type coupling the overall period of the system moves towards the perturbed oscillator. Though there is a period-buffering, the amplitudes of oscillators coupled through -OR- type logic are more sensitive to perturbations in the parameters associated with the promoter state dynamics than -AND- type. Further analysis shows that the period of -AND- type coupled dual-feedback oscillators can be tuned without conceding on the amplitudes. Using these results we derive the basic design principles governing the robust and tunable synthetic gene oscillators without compromising on their amplitudes.
Highlights
Transcription factors (TFs) regulate the quantitative levels of several proteins inside a living cell [1,2,3,4]
Theoretical framework of transcription factor gene oscillators The Goodwin-Griffith oscillator consists of a negatively selfregulated gene which codes for a transcription factor protein (Figure 2A)
The overall forward and reverse rate constants associated with the binding and unbinding of na numbers of end-product molecules with the respective cis-regulatory modules (CRMs) of the promoter of TF gene A are kaf (M{na s{1) and kar (s21) and the corresponding dissociation constant is defined as Karf ~kar kaf (Mna )
Summary
Transcription factors (TFs) regulate the quantitative levels of several proteins inside a living cell [1,2,3,4]. Feedback loops act as bistable switches and feedforward loops have been shown to act as efficient filters for transient external signals [8], [10,11,12]. Positive self-regulatory loops seem to play important roles in the maintenance of cellular memory [3] and subsequent reprogramming of the cellular states whereas negative auto regulatory loops have been shown [11] to speed up the response times against an external stimulus [8,9,10], [12]. Oscillatory loops drive the developmental as well as mitotic cell-cycle dynamics [13] and circadian-rhythms [14], [15] associated with the intracellular concentration of various types of proteins, metabolites and other cell-signaling molecules. Understanding of the detailed dynamics of oscillatory loops associated with the TF networks is a central topic in biophysics, synthetic and systems biology
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